Shar va uning kesimlari
![Geometriya
Mavzu: Shar va uning
kesimlari](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_1.png)
![Shar
Fazoning berilgan
nuqtadan, berilgan
masofadan katta
bo‘lmagan uzoqlikda
yotgan hamma
nuqtalaridan iborat
jismga shar deyiladi.](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_2.png)
![Berilgan nuqta shar-
ning markazi , berilgan
masofa sharning radiusi
deb ataladi. radius vatar
markaz
diametrSharning elementlari
Shar markazini shar sirtining istalgan nuqtasi
bilan tutashtiruvchi kesma ham radius deyiladi.](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_3.png)
![radius vatar
markaz
diametrSharning elementlari
Shar sirtining ikki
nuqtasini tutashtiruvchi
va sharning markazidan
o‘tuvchi kesma diametr
deyiladi.](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_4.png)
![Sharning chegarasi shar sirti yoki
sfera deb ataladi. Shar sirti yoki sfera
Sharning markazidan radiusga teng
masofa qadar uzoqlashgan hamma
nuqtalar sferaning nuqtalaridir.](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_5.png)
![Markazi nuqtada va
radiusi ga teng bo‘lgan
sferaning ixtiyoriy
nuqtasi koordinatalari
quyidagi tenglikni
qanoatlantiradi:( ?????? − ?????? )
??????
+ ( ?????? − ?????? )
??????
+ ( ?????? − ?????? )
??????
= ??????
?????? Sferaning tenglamasi
??????
??????
??????
??????
?????? ( ?????? ; ?????? ; ?????? )
?????? (?????? ; ?????? ; ?????? )](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_6.png)
![Markazi nuqtada va radiusi
ga teng bo‘lgan sferaning
ixtiyoriy nuqtasi koordinatalari
quyidagi tenglikni
qanoatlantiradi:??????
??????
+ ??????
??????
+ ??????
??????
= ??????
?????? Sferaning tenglamasi
??????
??????
??????
??????](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_7.png)
![Markazi nuqtada va radiusi ga teng
bo‘lgan shar ixtiyoriy nuqta-larining
koordinatalari quyidagi tengsizlikni
qanoatlantiradi:( ?????? − ?????? )
??????
+ ( ?????? − ?????? )
??????
+ ( ?????? − ?????? )
??????
≤ ??????
?????? Sharning tenglamasi](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_8.png)
![Shar va sfera aylanish jismlari
bo‘lib, mos ravishda yarim doira va yarim
aylanani diametri atrofida aylantirishdan
hosil qilinadi.](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_9.png)
![Bu doiraning markazi shar markazidan
kesuvchi tekislikka tushirilgan
perpendikulyar asosidan iborat. Sharni ixtiyoriy tekislik bilan
kesganda kesimda doira hosil bo‘ladi.](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_10.png)
![Radiusi ga teng shar markazidan
masofada bo‘lgan tekislik o‘tkazilgan
bo‘lsin.
Bu holda, agar bo‘lsa, tekislik va shar
umumiy nuqtaga ega emas. ??????
??????
??????
??????](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_11.png)
![Agar bo‘lsa, tekislik sharga
urinadi. ??????
??????
??????
??????](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_12.png)
![Agar bo‘lsa, tekislik sharni
radiusi bo‘lgan doira bo‘ylab kesib
o‘tadi. ??????
??????
?????? ??????
??????
??????
??????
??????](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_13.png)
![Sharning markazidan o‘tadigan
tekislik diametr tekisligi deyiladi.
Diametr tekisligining shar bilan kesimi
katta doira deyiladi. ??????
Sfera bilan kesimi katta aylana deyiladi.](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_14.png)
![Sharning ixtiyoriy diametr tekisligi
uning simmetriya tekisligidan iborat
bo‘ladi. ?????? ??????
??????
??????
?????? ?????? ?????? ??????
Sharning markazi uning simmetriya
markazidir.](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_15.png)
![1- masala
Sferaning radiusi ga teng. Sfera
markazidan masofada tekislik
o‘tkazilgan. Hosil bo‘lgan kesimning
yuzini toping.](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_16.png)
![Masalaning yechimi
Berilgan: ???????????? = ???????????? ????????????
??????
?????? ?????? ??????
?????? ??????
??????
= ?????? ????????????
??????
??????????????????????????????
= ?
Topish kerak:](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_17.png)
![????????????
??????
= ?????? ?????? ??????
??????
+ ?????? ?????? ??????
??????
??????
?????? ?????? ??????
?????? ?????? ??????
??????
= ????????????
??????
− ??????
??????
= ??????????????????
?????? ?????????????????????????????? = ?????? ?????? ??????
??????
?????? ?????? ??????
??????
= ????????????
??????
− ?????? ?????? ??????
??????
?????? ?????? ?????? = ???????????? ????????????
?????? ?????? = ?????? ?????? ?????? ?????? ?????? = ???????????? ????????????
?????? ?????????????????????????????? = ?????? ∙ ????????????
??????
= ?????????????????? ?????? ????????????
??????Javob:](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_18.png)
![2 - masala
Shar radiusi ga teng. Radius uchidan
burchak tashkil qiluvchi tekislik o‘tkazilgan.
Shar bilan tekislik hosil qilgan kesimning
yuzini toping.](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_19.png)
![Masalaning yechimi
Berilgan: ?????? = ????????????
??????
???????????? = ?????? ????????????
??????
??????????????????????????????
= ?
Topish kerak:
??????
?????? ?????? ?????? ???????????? ??????](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_20.png)
![?????? ?????? ?????? = ???????????? ∙ ?????????????????? ????????????
??????
??????
?????? ?????? ?????? ???????????? ??????
??????
??????
?????? = ?????? ∙
√ ??????
??????
= ?????? √ ??????
?????? ?????? ?????? = ?????? √ ?????? ????????????](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_21.png)
![??????
?????? ?????? ?????? ???????????? ??????Javob:
?????? ?????? = ?????? ?????? ??????
?????? ?????? = ?????? √ ?????? ????????????
?????? ?????????????????????????????? = ?????? ?????? ??????
??????
??????
??????????????????????????????
= ?????? ∙ ( ?????? √ ?????? )
??????
= ¿
¿ ???????????? ?????? ????????????
??????](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_22.png)
![3 - masala
va nuqtalar sfera diametrining uchlari
bo‘lsa,
sfera tenglamasini toping.](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_23.png)
![Masalaning yechimi
Berilgan: ?????? (?????? ; − ?????? ; ?????? )
?????? ( ?????? ; ?????? ; − ?????? )
Topish kerak:
??????
??????
??????
( ?????? − ?????? )
??????
+ ( ?????? − ?????? )
??????
+ ( ?????? − ?????? )
??????
= ??????
??????](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_24.png)
![?????? (?????? ; − ?????? ; ?????? ) ?????? ( ?????? ; ?????? ; − ?????? )
????????????
??????
= ( ?????? − ?????? )
??????
+ ( ?????? − (− ?????? ) )
??????
+ ( − ?????? − ?????? )
??????
????????????
??????
= ??????
??????
+ ??????
??????
+ ( − ?????? )
??????
= ?????? + ???????????? + ???????????? = ????????????
???????????? = √ ???????????? = ?????? √ ???????????? ?????? = ???????????? = ?????? √ ????????????
?????? =
??????
??????
=
?????? √ ????????????
??????
= √ ???????????? ?????? = √ ????????????](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_25.png)
![?????? (?????? ; − ?????? ; ?????? ) ?????? ( ?????? ; ?????? ; − ?????? )
?????? ( ?????? ; ?????? ; ?????? )= ?
?????? ( ?????? ; ?????? ; ?????? )= ?????? ( ?????? ; − ?????? ; ?????? ) ?????? = √ ????????????
( ?????? − ?????? )
??????
+ ( ?????? − ( − ?????? ) )
??????
+ ( ?????? − ?????? )
??????
= ( √ ???????????? )
??????
( ?????? − ?????? )
??????
+ ( ?????? + ?????? )
??????
+ ( ?????? − ?????? )
??????
= ????????????
Javob:](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_26.png)
![Mustaqil bajarish uchun topshiriqlar:
152-sahifa
510
512
514](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_27.png)
![Shar sirtidagi S nuqtadan o‘tib,
shu nuqtaga o‘tkazilgan radiusga
perpendikulyar bo‘lgan tekislik
sharning urinma tekisligi , nuqta
esa urinish nuqtasi deyiladi.
Urinma tekislik bilan shar faqat
bitta umumiy nuqtaga – urinish
nuqtasiga ega bo‘ladi.](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_28.png)
![Sharning urinma tekisligida yotib,
urinish nuqtasidan o‘tuvchi to‘g‘ri
chiziq shu nuqtada sharga
urinma deyiladi.
Urinma to‘g‘ri chiziq ham
shar bilan faqat bitta
umumiy nuqtaga - urinish
nuqtasiga ega bo‘ladi.](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_29.png)
![Ikki sferaning kesishishidan aylana
hosil bo‘ladi.
Kesishish nuqtasi faqat bitta nuqtadan
iborat sferalar bir-biriga urinadigan
sferalar deyiladi.](/data/documents/65f7ae8a-2ae5-467e-9cb7-92bd3e2b0da5/page_30.png)
Geometriya Mavzu: Shar va uning kesimlari
Shar Fazoning berilgan nuqtadan, berilgan masofadan katta bo‘lmagan uzoqlikda yotgan hamma nuqtalaridan iborat jismga shar deyiladi.
Berilgan nuqta shar- ning markazi , berilgan masofa sharning radiusi deb ataladi. radius vatar markaz diametrSharning elementlari Shar markazini shar sirtining istalgan nuqtasi bilan tutashtiruvchi kesma ham radius deyiladi.
radius vatar markaz diametrSharning elementlari Shar sirtining ikki nuqtasini tutashtiruvchi va sharning markazidan o‘tuvchi kesma diametr deyiladi.
Sharning chegarasi shar sirti yoki sfera deb ataladi. Shar sirti yoki sfera Sharning markazidan radiusga teng masofa qadar uzoqlashgan hamma nuqtalar sferaning nuqtalaridir.